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Pascal Marquet


The moist-air entropy can be used to analyze and better understand the general circulation of the atmosphere or convective motions. Isentropic analyses are commonly based on studies of different equivalent potential temperatures, all of which are assumed to fully represent the entropy of moist air. It is, however, possible to rely either on statistical physics or the third law of thermodynamics when defining and computing the absolute entropy of moist air and to study the corresponding third-law potential temperature, which is different from the previous ones. The third law assumes that the entropy for the most stable crystalline state of all substances is zero when approaching absolute zero temperature.

This paper shows that the way all these moist-air potential temperatures are defined has a large impact on (i) the plotting of the isentropes for a simulation of Hurricane Dumile, (ii) the changes in moist-air entropy computed for a steam cycle defined for this hurricane, (iii) the analyses of isentropic streamfunctions computed for this hurricane, and (iv) the computations of the heat input, the work function, and the efficiency defined for this steam cycle.

The moist-air entropy is a state function and the isentropic analyses must be completely determined by the local moist-air conditions. The large differences observed between the different formulations of moist-air entropy are interpreted as proof that the isentropic analyses of moist-air atmospheric motions must be achieved by using the third-law potential temperature defined from general thermodynamics.

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Pascal Marquet and Thibaut Dauhut


A careful reading of old articles puts Olivier Pauluis’s criticisms concerning the definition of isentropic processes in terms of a potential temperature closely associated with the entropy of moist air, together with the third principle of thermodynamics, into perspective.

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Pascal Marquet and Bjorn Stevens


A framework is introduced to compare moist “potential” temperatures. The equivalent potential temperature θ e, the liquid water potential temperature θ, and the entropy potential temperature θs are all shown to be potential temperatures, in the sense that they measure the temperatures of certain reference-state systems whose entropy is the same as that of the air parcel. They only differ in the choice of reference-state composition—θ describes the temperature a condensate-free state, θ e a vapor-free state, and θs a water-free state—required to have the same entropy as the given state. Although in this sense θ e, θ, and θs are all different flavors of the same thing, only θ satisfies the stricter definition of a “potential temperature,” as corresponding to a reference temperature accessible by an isentropic and closed transformation of a system in equilibrium; both θ e and θ measure the “relative” enthalpy of an air parcel at their respective reference states, but only θs measures air-parcel entropy. None mix linearly, but all do so approximately, and all reduce to the dry potential temperature θ in the limit as the water mass fraction goes to zero. As is well known, θ does mix linearly and inherits all the favorable (entropic, enthalpic, and potential temperature) properties of its various—but descriptively less rich—moist counterparts. All involve quite complex expressions, but admit relatively simple and useful approximations. Of the three moist “potential” temperatures, θs is the least familiar, but the most well mixed in the broader tropics, a property that merits further study as a possible basis for constraining mixing processes.

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